Rectangle inscribed in Triangle

Let PQRS be a rectangle inscribed in a triangle ABC(i.e P is in AC, Q in BC and R,S are in AB). Find the locus of points that are intersection of diagonals of the rectangle. (i.e find the locus of intersection of RQ and PS)

Hi. Well, it's not a homework problem, that's for sure. I haven't done much progress on this problem, seems quite hard. Or perhaps just my elementary geometry skills suck ? I've tried to somehow interpret this geometric problem in complex numbers' language, you know, but didn't really work as I thought. First I thought the locus should be a line, but now I doubt it. I think it's not. I may be wrong. Thank you !